Underrelaxed drained bulk modulus for fluid-saturated rocks in full frequency range

Abstract

Local flowing between cracks and pores is called squirt-flow that usually induce elastic moduli dispersion and waves attenuation. Expression of underrelaxed drained bulk modulus in full frequency range is derivated in this paper. Underrelaxed drained bulk modulus's real part increases with frequency, and underrelaxed drained bulk modulus's imagnary part is nonzero. This study also shows that liquid pressure in cracks equals to zero in the low-frequency limit, that is to say liquid pressure in cracks have sufficient time to relax and in this case the drained bulk modulus correspondents to Biot's static dry bulk modulus. In the high-frequency limit, the underrelaxed drained bulk modulus approximate to Mavko-Jizba's expression. The underrelaxed drained bulk modulus can be used to calculate fast P-wave and slow P-wave velocities and attenuation instead of static drained or dry bulk modulus in Biot's theory. © 2013 Acoustical Society of America.